Why is Sefer Bamidbar called 'Chumash ha'Pekudim'?
Rashi (in Sotah, 36b): Because it begins with the appointment of the Nesi'im of the tribes. 1
Shlah, based on Pesikta: It is because Bnei Yisrael are counted in it [at the beginning and towards the end].
And 'Pekidah' can mean 'appointment'.
What is the connection between the current Parshah to the previous one?
Ramban (in his Introduction to Sefer Bamidbar): Notwithstanding the break to present the laws of Shemitah and Yovel, 1 having discussed the Korbanos in Sefer Vayikra, the Torah now discusses the Ohel Mo'ed 2 - how they guarded it and its Keilim, how they encamped around it and how the people kept their distance, how the Kohanim behaved when they were encamped, when they carried it and whilst guarding it.
What sets apart the Mitzvos that are said in Sefer Bamidbar from those that were said previously?
Ramban: Or to the miracles that they experienced - in order to relate the wondrous deeds that Hashem performed with them (It is unclear why the Ramban does not include the incidents where they sinned and the punishments that they received?)
Ramban: With the exception of a few Mitzvos and matters of Korbanos, the details of which they were not commanded earlier.
Why did Hashem order the counting of Yisrael at this time?
Rashi: Because Hashem was coming to rest His Shechinah on them, 1 one month after the Mishkan was erected.
Rashbam: Because they were about to enter Eretz Yisrael, 2 and begin the conquest of the land and all those from the age of 20 (who were being counted) were eligible for conscription.
Seforno: To prepare them to enter Eretz Yisrael and to posses it without raising a sword. 3
Moshav Zekenim: [He would have counted them earlier, just] until now they were busy with building the Mishkan, erecting it, the Korbanos of the Nesi'im and Chanukas ha'Mizbe'ach. 4
See Sifsei Chachamim.
Rashbam See 10:11.
Seforno: Because had they not sinned by the Meraglim, the Kena'anim would all have fled - as some did anyway, possibly the Girgashi, as the Pasuk states in Yeshayah, 17:9. See also Rashi, Devarim, 1:8.
He counted them when they left Egypt and after they fell at the Eigel. Why did He find it necessary to count them at every opportunity?
Rashi: This is a sign that Hashem loves Yisrael. 1
Da'as Zekenim (2) Hadar Zekenim (2), both citing Bechor Shor: The previous counts did not detail the population of each Shevet.
Hadar Zekenim: They were not counted when they left Egypt, just the Torah said that there were about 600,000 men. This was the first count It is the same count mentioned in Pekudei, just it was mentioned there due to the calculation of the silver.
Moshav Zekenim: Hashem appointed Moshe over Bnei Yisrael. It is normal to count a flock when it is given to a shepherd, and when he returns them. 2
Ramban (45): Based on Iyov, 12:23, 5:18, that love is expressed by the fact that, although when He punishes the nations of the world, He destroys them, when He punishes Yisrael, He crushes them temporarily and withdraws.
I.e. Hashem counted Yisrael again (Perek 26) shortly before Moshe will die (27:13). (PF)
Why does the Torah see fit to mention the fact that this took place in the Ohel Mo'ed?
Ramban (introduction to Sefer Bamidbar): Having interrupted the sequence with the Mitzvos concerning Shemitah and Yovel, which were told to Moshe on Sinai, 1 it found it necessary to mention that, from now on, the Mitzvos will be said in the Ohel Mo'ed, like those that were said from the beginning of Vayikra until Parshas B'har.
Rashbam: In connection with all the commands that Hashem issued in the first year - before the Mishkan was erected, the Torah writes "Har Sinai"; 2 Once the Mishkan was erected, it writes "b'Midbar Sinai b'Ohel Mo'ed".
Rashbam: See, for example, Shemos 31:18. This is also borne out by the fact that, later, in 3:1. the Torah inserts the words "V'eileh Toldos Aharon u'Moshe ... b'Yom Diber es Moshe ... b'Har Sinai", which it adds because once the Mishkan was erected, Aharon's children no longer numbered four, but two, as the Torah stresses there, in Pasuk 4.
What is the difference between the Mitzvos that were said on Har Sinai and those that were said in the Ohel Mo'ed?
Ramban (introduction), Moshav Zekenim: There is no basic difference between them. The Torah confines the Shechinah to an enclosed space in the Mishkan (Shemos 19:12), just as it was on Har Sinai; 1 It commands that 'a Zar who approaches will die' (later, 1:51, 18:7) just as it did on Har Sinai; 2 'Not to come and watch as the Kodesh is put away' (later, 4:20), just as they were commanded at Har Sinai 3 and that the Kohanim should guard the Mishkan and the Mizbe'ach (18:5), just as they were at Har Sinai. 4
Why does the Torah detail the exact date?
Rosh: A parable for this is a man who married a woman and did not write a Kesuvah, and divorced her without a Get. He did similarly with two other women. He then saw a woman of great lineage, and said that he will write a Kesuvah detailing the place and date. Hashem created His world, and Dor ha'Mabul and Dor ha'Flagah, Anshei Sedom, and did not specify when they were created or removed. He said that Yisrael, the children of Avraham, Yitzchak and Yakov, will be different.
Why does the Torah mention that this was in the Midbar?
Moshav Zekenim, Rosh: Torah was given via three Hefker matters
Moshav Zekenim: However, one who teaches may receive wages for what he could have earned; teachers of children were paid from Terumas ha'Lishkah. Also Ta'anis 24a implies that one may be paid to teach children.